Please show all steps, Integration involving exponential or logarithmic functions.

a$){\displaystyle \underset{0}{\overset{1}{}}}{e}^{x}dx$

b$){\displaystyle \underset{0}{\overset{1}{}}}x{e}^{x^2}dx$

c$){\displaystyle \underset{1}{\overset{2}{}}}\frac{1}{x}dx$

d$){\displaystyle \underset{1}{\overset{2}{}}}\frac{2x}{x^{2}4}dx$

Integration by parts

a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xsinh(x)dx$

b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}ta{n}^{-1}(x)dx$

c$){\displaystyle \underset{1}{\overset{3}{}}}{x}^{3}lnxdx$

d$){\displaystyle \underset{0}{\overset{x^2}{}}}sin\sqrt[\phantom{2}]{x}dx$